Question 1

The personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:  What is the calculated value of chi-square?

Accepted Answer

A)   1.0
B)   0.5
C)   0.8
D)   8.0
E)   None of these statements are correct

Question 2

The chi-square distribution is:

Accepted Answer

A)   positively skewed.
B)   negatively skewed.
C)   normally distributed.
D)   negatively or positively skewed.
E)   None of these statements are correct.

Question 3

The personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:  What kind of frequencies are the numbers 12, 9, 11, 10, and 9 called?

Accepted Answer

A)   Acceptance
B)   Critical value
C)   Expected
D)   Observed
E)   None of these statements are correct

Question 4

i. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies.
Ii)  For a goodness-of-fit test, the following are possible null and alternate hypotheses. Null: Sales are uniformly distributed among the five locations. Alternate: Sales are not uniformly distributed among the five locations.
Iii)  The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 5

i. The null hypothesis in the goodness-of-fit test is that there is no difference ii. The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test.
Iii)  The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 6

A school is trying to determine if there is a relationship between gender and which of its 3 programs that students enrol. It was observed that 20 females enrolled in accounting, 15 in finance and 25 in marketing. For males, 10 enrolled in accounting, 20 enrolled in finance and 15 enrolled in marketing. Can we conclude that there is a relationship between gender and program? Use the 0.05 significance level.

Accepted Answer

A)   There is no evidence of a relationship between gender and program of study.
B)   There is evidence of a relationship between gender and program of study.
C)   Not enough information is given to reach a conclusion.
D)   None of the above.

Question 7

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results.  What is the alternative hypothesis?

Accepted Answer

A)   The letter grades are evenly distributed.
B)   The letter grades are not evenly distributed.
C)   The letter grades are normally distributed.
D)   The letter grades are not normally distributed.
E)   The letter grades are unfairly distributed.

Question 8

i. Tests of hypotheses for nominal or ordinal levels of measurement are called nonparametric or distribution-free tests.
Ii)  There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on. 
iii. The shape of the chi-square distribution depends on the size of the sample.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 9

Six people have declared their intentions to run for a trustee seat in the next local election. A political poll is conducted during the campaign among 1,020 voters to determine if there is any clear preference among the voters. The responses are shown below.  What is the critical value at the 1% level of significance?

Accepted Answer

A)   6.635
B)   9.210
C)   11.345
D)   13.277
E)   15.086

Question 10

i. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.
Ii)  The claim that "male and female University of Toledo students prefer different parking lots on campus" is an example of a chi-square null hypothesis.
Iii)  For contingency table analysis using the chi-square test, multiplying the number of rows minus 1 by the number of columns minus 1 will give you the degrees of freedom.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (iii)  is a correct statement but not (i)  or (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 11

i. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies.
Ii)  For a goodness-of-fit test, the number of degrees of freedom is determined by k - 2, where k is the number of categories
Iii)  The sum of the expected frequencies in a goodness-of-fit test need not equal the sum of the observed frequencies.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   (i)  is a correct statement, but (ii)  and (iii)  are false.

Question 12

The chi-square distribution becomes more symmetrical as:

Accepted Answer

A)   number of variables increase.
B)   the chi-square value increases.
C)   degrees of freedom decrease.
D)   degrees of freedom increase.
E)   None of these statements are correct.

Question 13

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?

Accepted Answer

A)   1.1
B)   3.9
C)   5.0
D)   5.5
E)   None of these statements are correct

Question 14

A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows:  
What is the critical value at the 0.01 level of risk?

Accepted Answer

A)   7.779
B)   15.033
C)   13.277
D)   5.412
E)   None of these statements are correct

Question 15

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results.  What is the expected number of C's?

Accepted Answer

A)   39.25
B)   34.13
C)   13.59
D)   30.00
E)   15.87

Question 16

Recently, students in a marketing research class were interested in the driving behaviour of students. Specifically, the marketing students were interested if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students:  The null hypothesis for the analysis is:

Accepted Answer

A)   There is no relationship between gender and speeding.
B)   The correlation between gender and speeding is zero.
C)   As gender increases, speeding increases.
D)   The mean of gender equals the mean of speeding.

Question 17

i. Small differences between observed and expected frequencies are due to chance. 
ii. The chi-square distribution with large degrees of freedom approaches a normal distribution. 
iii. The chi-square distribution is positively skewed.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 18

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below.  Which of the following statements are correct?

Accepted Answer

A)   Property Front-footage and Opinion on the street widening are related when tested at the 0.10 level of significance
B)   Property Front-footage and Opinion on the street widening are related when tested at the 0.05 level of significance
C)   Property Front-footage and Opinion on the street widening are not related when tested at the 0.05 level of significance
D)   Property Front-footage and Opinion on the street widening are not related when tested at the 0.20 level of significance
E)   Property Front-footage and Opinion on the street widening are unrelated when tested at any level of significance

Question 19

i. A goodness-of-fit test is a nonparametric test involving a set of observed frequencies and a corresponding set of expected frequencies.
Ii)  For a goodness-of-fit test, the following are possible null and alternate hypotheses: Null: Sales are uniformly distributed among the five locations; Alternate: Sales are not uniformly distributed among the five locations.
Iii)  In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed set of observations "fits" an "expected" set of observations.

Accepted Answer

A)   (i) , (ii)  and (iii)  are all correct statements
B)   (i)  and (ii)  are correct statements, but not (iii) .
C)   (i)  and (iii)  are correct statements but not (ii) .
D)   (ii)  and (iii)  are correct statements but not (i) .
E)   All statements are false

Question 20

Which of the following are correct statements regarding the goodness-of-fit test?

Accepted Answer

A)   Data may be of nominal scale
B)   Population must be normal
C)   All the expected frequencies must be equal
D)   All of the above are true
E)   None of these statements are correct are true

Exam 14: Chi-Square Applications for Nominal Data

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i. Small differences between observed and expected frequencies are due to chance. ii. The chi-square distribution with large degrees of freedom approaches a normal distribution. iii. The chi-square distribution is positively skewed.

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The chi-square distribution is:

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A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows: What is the critical value at the 0.01 level of risk?

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The chi-square distribution becomes more symmetrical as:

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Which of the following are correct statements regarding the goodness-of-fit test?

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Exam 14: Chi-Square Applications for Nominal Data

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i. Small differences between observed and expected frequencies are due to chance. ii. The chi-square distribution with large degrees of freedom approaches a normal distribution. iii. The chi-square distribution is positively skewed.

Correct AnswerverifiedShow Answer

The chi-square distribution is:

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A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows: What is the critical value at the 0.01 level of risk?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The chi-square distribution becomes more symmetrical as:

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Which of the following are correct statements regarding the goodness-of-fit test?

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